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The topographical factor

Although slope has a powerful influence on erosion, the presence of erosion and heavy runoff on gentle slopes (2% in the Sahel or on European uplands) indicates that this phenomenon can occur without any need for a steep slope: the action of rain is enough (Fauck 1956, Fournier 1967).

The influence of slope on the development of hillsides is well known to geomorphologists, so that some of them would even specify the age of the landscape in terms of the gradient and shape of its slopes. Steep slopes and deep valleys are found in a young landform such as the Alps, whereas in an adult and senile landform - as on the old African continent - there are plateaux, gentle slopes, pediments and vast peneplains.

Slope intervenes in erosion in terms of its form, gradient, length and position.

THE FORM OF SLOPES

Estimating the influence of the concavity, convexity, regularity or warp of a slope is a very delicate procedure. This factor is too often neglected, which in large part explains why authors come up with such divergent results. As eroding plots age and are exposed to severe erosion, they become more and more concave, since the base of the plot stays fixed (the runoff channel) and the middle of the plot erodes more quickly than the top. This means that each year the slope of the plots must be readjusted so that the results are not falsified by default. According to Wischmeier (1974), with a smooth average slope, sediment transport is reduced on a warped or concave slope (due to localized sedimentation), but increased on a convex slope due to the gradient of the steepest portion. The presence of concave slopes in a landscape indicates that there must be trapping, siltation and colluvial deposit in the valley. In general, erosion on the hillside exceeds the sediment transport in the river although this is not the case in the Mediterranean area, where the main cause of sediment transport is the energy and volume of runoff (Heusch 1971; Arabi and Roose 1989).

SLOPE GRADIENT

As the gradient increases, the kinetic energy of rainfall remains constant, but transport accelerates toward the foot as the kinetic energy of the runoff increases and outweighs the kinetic energy of the rainfall when the slope (S) exceeds 15%. In 1940 Zingg showed that soil loss increases exponentially with the slope gradient. In the United States the exponent is 1.4:

E = K S^1.4

Hudson and Jackson (1959) emphasized that in Central Africa aggressiveness of climate increases the effect of slope over what is found in the United States, so that they obtained exponents averaging about 1.63 on complete rotations (including grassland and fallow periods), and up to 2.02 on clayey soil and 2.17 on sandy soil under extensive maize cropping. An exponent in the region of 2 would seem more likely under African conditions (Hudson 1973).

At Séfa in Senegal, Roose (1967) found that erosion and runoff increase very quickly with minor variations in slope (0.5%) (see Table 10).

In Côte d'Ivoire on food crops between 1964 and 1976, Roose (1980a) obtained an exponent higher than 2 for extensive crops that provide little cover, such as groundnut, maize and cassava.

On the other hand, in Nigeria Lal (1976) found that erosion increases with slope according to an exponential curve of 1.2 on modified ferralitic soil enriched with gravel (alfisol) when the soil is bare, but that soil loss is independent of slope (from 1 to 15%) if crop residues are left on the surface. Runoff as such would depend more on the hydrodynamic properties of the soil than on the slope itself.

TABLE 11
Runoff (KR %) and erosion (t/ha) on bare soil and under pineapple as a function of crop residues (cf. Roose, 1980a)

Adiopodoumé: 12 cases of erosion under natural rainfall 1975-1977: 16-month cycle, ferralitic soil, slopes 4, 7, 20%

RUNOFF (KR % of rainfall)
1st cycle: 3337 mm rainfall	Bare soil	Burnt off	Dug in	Mulch	Average/slope
Slope 4%	44.6	7.3	1.7	0.9	13.6
7%	34.7	4.4	1.0	0	10.0
20%	29.3	7.5	3.4	0.1	10.3
Average/treatment	36.2	6.4	2.0	0.6	11.3

Notes:

Runoff does not necessarily increase with slope.
Strong influence of crop residues if planting date is close to critical periods (cycles).

EROSION (t/ha)
	Bare soil	Burnt off	Dug in	Mulch	Average/slope
Slope 4%	45	1.2	0.7	0.1	11.8
7%	136	4.1	0.45	0	35.2
20%	410	69	33.2	1	128.3
Average/treatment	197	24.8	11.5	0.38	58.4

Notes:

Planting in August; pineapples provide good soil cover before the June rains - little erosion, regardless of type of treatment.
Slope has a strong effect on erosion

TABLE 12
Erosion t/ha/yr and runoff (KR %) as a function of slope under forest, crops and bare soil at the ORSTOM centre at Adiopodoumé in southern Côte d'Ivoire (cf. Roose 1973)

Adiopodoumé 1956-1972.
Ferralitic soil on clayey-sandy tertiary material.
Mean rainfall: 2100 mm.

Slope %	Erosion t/ha/yr			Runoff KR %
	forest	bare soil	crop	forest	bare soil	crop
4.5	-	60	19	-	35	16
7	0.03	138	75	0.14	33	24
23	0.1	570	195	0.6	24	24
65	1.0	-	-	0.7	-	-

On erosion plots with slopes of 4, 7 and 20% at the ORSTOM centre at Adiopodoumé in southern Côte d'Ivoire, Roose (1980a) compared erosion on bare soils and on soils covered with pineapple plantations, residues having been burnt, ploughed in, or left on the surface. He recorded a more than proportional increase of erosion with the slope, but highlighted the existence of gradient thresholds below which erosion is small but above which it suddenly increases. For example, when residues are ploughed in, erosion is very slight on slopes of under 7%, but beyond 20% it quickly moves far above the tolerance level. If residues are left on the surface as a mulch, erosion is negligible even beyond 20%. Similarly, during the second cropping cycle, planting took place in August so that the pineapple plants provided good cover to the soil before the aggressive rains of the following June; very little erosion was recorded, whatever the slope and the way crop residues were handled. These results clearly indicate the existence of interaction between the effect of slope, plant cover and treatment of crop residues (Table 11). It has been noted in West Africa that natural vegetation that has survived fires protects landforms very well (Roose 1971, Avenard and Roose 1972). The same can be seen in southern Côte d'Ivoire, where there are slopes of over 65% on sandy-clayey ferralitic soil protected by dense secondary forest. If forest is cleared manually without destroying the root network that provides cohesion to the topsoil, the soil can resist the aggressiveness of rainfall for one or two years. However, if forest or savannah is cleared mechanically, scouring the fertile topsoil, erosion and runoff assume catastrophic proportions, further aggravated on steep slopes.

Adiopodoumé has three plots under closed secondary forest, and three cultivated in 1966/67, maintained under bare fallow, and tilled before the rainy season from 1968 to 1972. Slopes varied from 4.5 to 65%. Table 12 shows average soil losses (in t/ha/yr) and runoff (as a percentage of annual rainfall) recorded during the period 1956 to 1972 (Roose, 1973).

Erosion is seen to increase proportionately faster than slope, and faster under crops than on bare soil. Under crops (cassava followed by groundnut), if the average erosion on a 4.5% slope is taken as the basis (E = 18.8 t/ha/yr soil loss increases fourfold when the slope rises to 7% (i.e. 1.5 times steeper) and another fourfold when it rises to 23% (i.e. 5.1 times steeper than the control plot). Erosion increases more slowly on a bare plot, but starts higher (E = 60 t/ha/yr It seems clear that on a steep slope there is an interaction between the effects of slope and the decrease in plant cover resulting from water stress and mineral deficiency in plants growing on steep eroded slopes. Alongside this quantitative aspect, the forms of erosion change with the slope and the soil profile. On a gentle slope (4%) raindrop energy dislodges aggregates and releases fine particles. Stable suspensions of colloids may travel long distances through the drainage system. Sand, on the other hand, collects on the soil surface, giving it a striped appearance with alternating dark bands (from stripped soil in relief) and yellow streaks (from sand in the grooves). The soil surface is almost flat on 4% slopes, but on a 7% slope, these lower areas deepen into widened rills into which sand in the washload settles. Microcliffs and small pedestals (2-4 cm) appear, which clearly show the extent of the scouring damage caused by sheet erosion. Lastly, on slopes of more than 20%, the runoff evacuation system removes particles of all sizes (up to 5 or 10 mm in diameter) and digs out grooves, so that the soil surface becomes extremely uneven, with deep rills (5-20 cm) and numerous humps chiselled by rain and runoff and protected by objects such as seeds, roots, leaves, bits of pottery and even hardened or crusted clods. In the United States Smith and Wischmeier (1957) have shown that on plots with a slope of 3 to 18% exposed to natural rainfall for 17 years, a second-degree equation works better than the logarithmic functions proposed by other American scientists, though these are in fact very close. This equation is:

where E, erosion, is expressed in t/ha, S, slope gradient, in %, and L, slope length, in feet (Figure 22).

FIGURE 22 Topographical factor (cf. Wischmeier and Smith 1978)

Wischmeier (1966) has shown that runoff usually increases with the slope on small plots, but that the increase varies with soil surface roughness and water-retention capacity (type of crop and saturation level before the rain).

In Côte d'Ivoire, the runoff/erosion duo behaves in a very different manner with respect to slope. At Adiopodoumé under crops, the runoff coefficient reaches 16% on a 4.5% slope, and stabilizes at around 24% on plots with a 7 or 23% slope. On bare fallow ground, runoff decreases noticeably (35, 33, 24%) when the slope increases from 4 to 7 and 23%, and this phenomenon has been confirmed over years of trials. This decrease in runoff as the slope increases is seen not only with average runoff coefficients, but also with maximum coefficients when the soil is saturated (KR_max = 98, 95, 76%). These trends were confirmed in subsequent years (1975-1977) under pineapple (Table 11). On bare soil runoff dropped from 44 to 35 and 29% as the slope increased from 4 to 7 and 20%. Under pineapple, runoff increased slightly or even decreased depending on how crop residues were handled. Here again, there is interaction between the slope and the condition of the soil surface as these affect runoff.

Hudson (1957) had already noted these phenomena in what was then Rhodesia, where he observed that erosion increases exponentially with slope, but that runoff increases rapidly at first (up to roughly 2% of slope) and then stabilizes.

In Nigeria too, Lal (1975) observed that runoff stabilized above a certain gradient depending on the way crop residues were used and on soil type.

The decrease in the runoff coefficient on bare soil may be explained, at least partially, by the following factors (Roose 1973):

• The sloping surface exposed to the rain increases as the slope grows steeper. In other words, if the area of the plot is field-measured without taking account of the vertical component, there will be an error of 0.3% for a 4.5% slope, 0.7% for a 7% slope, and 2% for a 20% slope.

• As the slope increases, the type of erosion changes, chiselling the ground into different shapes and thereby increasing the surface area - and hence the number of pores that can absorb water, at least in the initial phase.

• When the slope is gentle, runoff energy is too weak to carry relatively coarse sandy particles very far. When it rains, these are released by the splash effect and then slowly carried downhill. As they move they may be drawn in by pores and block them. They also go to form microstrata - the phenomenon of glazing familiar to agronomists. On a steep slope, however, all particles detached by the rain's force are carried off the plot, and it may be surmised that more pores stay open, for erosion scours the soil surface heavily. In any case, it has been observed in the field that crust formation occurs much more slowly on steep slopes and that hoeing has much longer-lasting effects than on gentle slopes.

• Lastly, the hydraulic gradient increases in line with the topography; i.e. steep slopes drain faster than gentle ones.

If erosion increases exponentially with slope despite a decrease in runoff, this is because the total sediment transport (suspended load + bedload) increases substantially with the slope.

As early as 1948, Woodruff in the United States showed that while the contribution of the kinetic energy of raindrops is of primary importance on a gentle slope, it is secondary to runoff energy over a 16% gradient. Heusch (1969, 1970, 1971) then showed that on pre-Rif marls in Morocco, erosion and runoff are sometimes affected more by position in the toposequence than by gradient. On the vertisol toposequence on marl, erosion and runoff readings increase at the foot of the slope, where the gradient decreases. This would be due to very marked phenomena of oblique drainage in these soils that are fissured down to the weathering level of the nearly impermeable marry rock. On a steep slope at the top of the hill (concave slope), rain infiltrates directly as far as the impermeable level, and then drains quickly down to the foot of the hill (gentle slope), where it re-emerges (Roose 1971). And this is where the gullies start that then climb back up to attack hills in regressive (headward) erosion. As Heusch (1971) has rightly pointed out, the steeper the topography, the steeper the hydraulic gradient. This means that water circulates quickly inside the soil, thus allowing the soil to reabsorb a certain amount of water before saturation. The soil on steep slopes and hilltops will dry out quicker, thus producing less runoff. In marry landscapes with steep slopes, erosion consists mainly of undermined banks, wandering wadis, gullying and landslides (Heusch 1971).

Somewhat similar processes have been described and studied on the Sudanian savannahs of central and western Côte d'Ivoire by a multi-disciplinary ORSTOM team (Valentin, Fritsch and Planchon 1987). The red gravelly ferralitic soils at the top of the toposequence are resistant and permeable so that only rarely are any significant traces of erosion found here. Ferruginous tropical hillsides are already more fragile, with small, discontinuous gullies, while larger gullies form on the sandy hydromorphic lowlands, growing in size as they move back up the landscape. Although these sequences in a Sudanian region operate very differently from those of marls in a Mediterranean region, topographical position often seems significant in explaining the development of erosion.

SLOPE LENGTH

In theory, the longer the slope, the more runoff will accumulate, gathering speed and gaining its own energy, causing rill erosion and then more serious gullying Thus, Zingg (1940) found that erosion increases exponentially (exponent = 0.6) with the length of the slope. Hudson (1957 and 1973) considered that a higher exponent value is more appropriate in tropical regions. Wischmeier, Smith and Uhland (1958) examined 532 annual results on erosion plots, and concluded that the ratio between erosion and length of slope varies more from year to year than from one site to another; the value of the exponent (from 0.1 to 0.9) is strongly affected by changes in soil, plant cover, use of crop residues, etc. Then in 1956 a research team from Purdue University, Nebraska, USA, decided to adopt an exponent of 0.5 to express the average influence of length of slope on soil loss for current field work. The influence of slope length on runoff is still less clear, being sometimes positive, sometimes negative, sometimes nil, depending on the prior moisture and condition of the soil surface (Wischmeier 1966).

At Séfa in Senegal (Roose 1967) three plots with a 1.25% slope were compared. On one plot, twice as long as the others, the crops of the other two plots were alternated (strip cropping in the direction of the slope). In general, runoff was weaker on the long plot (KR = 19% as against 21%), while erosion was higher (E = 6.08 as against 5.55 t/ha/yr) than on the two short plots, but the difference in behaviour was barely significant.

At Agonkamé in southern Benin (Verney, Volkoff and Willaime 1967, Roose 1976), conclusions from two neighbouring plots (slope = 4.5%) also failed to clearly confirm any increase in erosion with length of slope. Under natural thicket, erosion and runoff were weaker on the long slope (60 m), while the following year, on cleared land with stumps removed, runoff on the two plots was similar, while erosion on the shorter plot (30 m) was much greater than on the longer plot (E = 27.5 as against 17 t/ha/yr). At Boukombé in northern Benin (Willaime 1962), observations on three plots under millet 21, 32 and 41 metres long with a 3.7% slope showed scarcely any difference in runoff (KR = 4%) or erosion (E = 0.8, 1 and 0.7 t/ha). The influence of length of slope is therefore neither consistent nor particularly strong.

In Côte d'Ivoire, Lafforgue and Naah (1976) simulated 12 rainfalls totalling 652 mm for an aggressiveness index of 1161 on four plots with a 6% slope on former grassland. The soil was sandy-clayey and all plant debris was carefully removed from the land. When length increased from 1 to 2 to 5 and 10 metres, runoff changed from 27 to 29 to 23 to 20%, but erosion increased from 8 to 8.6 to 11.3 to 13.7 t/ha/yr - because turbidity (the solids suspended in the water) increased from 5 to 27 g/l. On these relatively short slopes, runoff decreased, while erosion and sediment load increased as the slope lengthened. However, there is no proof that there will be a proportionate increase in erosion when the length of the slope is increased to 50, 100 or 150 metres.

In the United States, Meyer, Decoursay and Romkens (1976) studied the effect of slope length on three sites with varying susceptibility to rill erosion. They showed that the effect of slope length was felt after a certain distance and that the speed of increase in erosion varied depending on soil susceptibility to rill erosion. Here again there is an interaction between the effect of slope length and soil sensitivity to rill erosion (Figure 23).

Ramser's equation was developed to calculate the gap between two erosion control structures. In practice, soil conservation engineers have adapted Ramser's equation, linking the difference in height between two erosion control structures (H in metres) directly to the gradient of the slope (S in %) while ignoring any interaction with soil cover and production system.

Ramser's equation: H (metres) = 0.305 (a + [S%/b]) (1)

a = 2
b varies from 2 to 4 if the climate is more aggressive

where a and b are parameters made to vary empirically by 25% depending on climatic aggressiveness or specific erosion risks (see Figure 24).

According to Figure 24 (taken from Combeau 1977), on a 10% slope:

- in Guinea, aggressive climate, H = 1.37 m, and gap = 14 m
- in Burkina Faso, less aggressive, H = 1.62 m, and gap = 16 m
- in Tunisia, H = 3 m, and gap = 30 m.

FIGURE 23 Effect of length of slope on three sites of varying susceptibility to rill erosion (cf. Meyer, Decoursay and Romkens 1976)

Rillability may be estimated by measuring:

- resistance to shearing stress
- volume of overland flow
- variations according to the drop test.

The structural stability of clods maintains:

+ a high degree of roughness
+ a high degree of turbulence
hence a higher untiary load.

Ramser's equation is far from complete, since it takes no account only of slope as a percentage (see Figure 24).

Ramser's equation is in fact far from complete, since it takes no account of possible interactions between the effects of slope, soil type, condition of surface and topographical position. It has even been seen that slope length has no apparent effect on erosion at certain stations in Africa.

There is little point in developing models that take account of slope length. Advice on field observation of the birth of rills would be preferable, allowing farmers to build erosion control structures at intervals reasonable from the technical standpoint and affordable for the farmer (5-50 m).

In Algeria, Saccardy (1950) used an assessment of peak rainfall intensity of about 3 mm/min over half an hour, and proposed for slopes of.

< 25 % H³ = 260 S (2)
> 25 % H² = 64 S (3)

where H is the difference in altitude between two bunds (in metres), and S is the slope of the land (as a percentage).

FIGURE 24 Various formulae linking the gap between erosion control structures and slope gradient (%) depending on country where applied (cf. Combeau 1977)

1. Application of Ramser's equation H = 0.305 12 + [S/4]) in Congo and Guinea.
2. Application of Ramser's equation H = 0.305 (2 + [S/3]) in less dangerous conditions.
3. Highly eroded soil very much reduced spacing, Burkina Faso (Ouahigouya), Mali (Sikasso).
4. Another proposal for Burkina Faso (Ouahigouya).
5. Another proposal for Burkina Faso (Boulbi).
6/7/8. Various proposals for Boukombé (Benin).
7. Dabou terraces (Côte d'Ivoire) and contour hedges.
9. Ramser's equation modified (South Africa).
10. Saccardy's equation (Algeria) H³ = 260 S + 10.
11. Bugeat's equation (Tunisia) H = 2,20 + 8 S.
12. Washington State equation (USA) H = 0,305 (0,58 + [S/1,7]).

Distances between erosion control structures according to Saccardy's equations (cf. Heusch 1986)

if slope < 25% H3 = 260 S
if slope > 25% H2 = 64 S

S%	0.03	0.05	0.10	0.15	0.20	0.25	0.30	0.35	0.40	0.45	0.50
dH (m)	1.98	2.35	2.96	3.39	3.73	4.01	4.38	4.73	5.06	5.37	5.66
dist. (m)	66.0	47.10	29.80	22.90	19.00	16.50	15.20	14.30	13.6	13.1	12.7

According to Heusch (1986), "There is no theoretical or practical justification for these formulae''. Wischmeier's SL factor for-the distance given by Saccardy's equation is not constant, but increases progressively from 0.4 for a 3% slope 66 m long, to 11 for a 50% slope and a gap of 12.7 m. At the very most, it can be agreed that Formula 3 can also be written:

H.C = 64

where C is a coefficient depending on local conditions, particularly climate,

which is the same as saying that the energy comes from the runoff if the slope is 25% or more.

This uncertainty over the influence of slope length on sheet and rill erosion throws fresh doubt on the generalized use of erosion control techniques such-as terracing, bunds and diversion channels which are too often indiscriminately applied in very different climates. While terracing is justified in a sub-desert environment where rainfall is below 400 mm/yr, it may be best replaced by biological methods in regions where vegetation can cover the soil and intercept the rain (Roose 1974). From a scientific viewpoint, the topographical factor and its multiple interactions should be further investigated and more clearly defined, for the influence of slope is not independent of plant cover, cropping techniques, soil type and probably climate (Roose 1973; 1977). However, until sufficient data are available, Wischmeier's topographical index or an exponential equation such as SL = C × L^0.5 × S^1.2-2, where L is length of slope in metres, and S the gradient in percent, can be relied upon. It should be satisfactory in most cases (Hudson 1973; Roose 1977).

In practice, rather than systematically applying models developed to some extent for other physical and human circumstances, the best approach seems to be a compromise between (a) field observation on the distance after which rill erosion develops, and (b) how many obstacles the farmers can accept on their land.

Consequences for erosion control Reduction of gradient was generally more effective than reduction of length of slope in controlling sheet and rill erosion. However, it does appear that under major crops the land must be partitioned with linear structures - semi-pervious microdams - which allow a reduction in runoff energy while encouraging the evacuation of water to the bottom of well-protected banks. This means that the ill effects of slope length can all be countered by building erosion control structures; all interactions of factors concerning the condition of the surface must be brought into play, especially encouraging roughness of soil and plant cover on cultivated fields between semi-pervious filtering structures. This will reduce the effect of slope length and gradient on erosion. It should be noted that slope length has little effect on sheet erosion because the speed of sheet runoff is kept down by the roughness of the soil, whereas it may have a significant effect on rill erosion.

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